FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3100853638> ?p ?o ?g. }

• W3100853638 endingPage "349" @default.
• W3100853638 startingPage "323" @default.
• W3100853638 abstract "Abstract Building upon the recent results in [M. Focardi and E. Spadaro, On the measure and the structure of the free boundary of the lower-dimensional obstacle problem, Arch. Ration. Mech. Anal. 230 2018, 1, 125–184] we provide a thorough description of the free boundary for the solutions to the fractional obstacle problem in <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msup> <m:mi>ℝ</m:mi> <m:mrow> <m:mi>n</m:mi> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msup> </m:math> {mathbb{R}^{n+1}} with obstacle function φ (suitably smooth and decaying fast at infinity) up to sets of null <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msup> <m:mi mathvariant=script>ℋ</m:mi> <m:mrow> <m:mi>n</m:mi> <m:mo>-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msup> </m:math> {{mathcal{H}}^{n-1}} measure. In particular, if φ is analytic, the problem reduces to the zero obstacle case dealt with in [M. Focardi and E. Spadaro, On the measure and the structure of the free boundary of the lower-dimensional obstacle problem, Arch. Ration. Mech. Anal. 230 2018, 1, 125–184] and therefore we retrieve the same results: (i) local finiteness of the <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mi>n</m:mi> <m:mo>-</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:math> {(n-1)} -dimensional Minkowski content of the free boundary (and thus of its Hausdorff measure), (ii) <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msup> <m:mi mathvariant=script>ℋ</m:mi> <m:mrow> <m:mi>n</m:mi> <m:mo>-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msup> </m:math> {{mathcal{H}}^{n-1}} -rectifiability of the free boundary, (iii) classification of the frequencies and of the blowups up to a set of Hausdorff dimension at most <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mi>n</m:mi> <m:mo>-</m:mo> <m:mn>2</m:mn> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:math> {(n-2)} in the free boundary. Instead, if <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>φ</m:mi> <m:mo>∈</m:mo> <m:mrow> <m:msup> <m:mi>C</m:mi> <m:mrow> <m:mi>k</m:mi> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mi>n</m:mi> </m:msup> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> {varphiin C^{k+1}(mathbb{R}^{n})} , <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>k</m:mi> <m:mo>≥</m:mo> <m:mn>2</m:mn> </m:mrow> </m:math> {kgeq 2} , similar results hold only for distinguished subsets of points in the free boundary where the order of contact of the solution with the obstacle function φ is less than <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>k</m:mi> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> {k+1} ." @default.
• W3100853638 created "2020-11-23" @default.
• W3100853638 creator A5027009955 @default.
• W3100853638 creator A5039149789 @default.
• W3100853638 date "2020-11-07" @default.
• W3100853638 modified "2023-09-24" @default.
• W3100853638 title "The local structure of the free boundary in the fractional obstacle problem" @default.
• W3100853638 cites W1528923274 @default.
• W3100853638 cites W1670380698 @default.
• W3100853638 cites W1822946441 @default.
• W3100853638 cites W1970161690 @default.
• W3100853638 cites W1998891015 @default.
• W3100853638 cites W2006455026 @default.
• W3100853638 cites W2025104304 @default.
• W3100853638 cites W2060200425 @default.
• W3100853638 cites W2062517214 @default.
• W3100853638 cites W2073670753 @default.
• W3100853638 cites W2074457835 @default.
• W3100853638 cites W2130440873 @default.
• W3100853638 cites W2131440582 @default.
• W3100853638 cites W2168741104 @default.
• W3100853638 cites W2810469877 @default.
• W3100853638 cites W2962740412 @default.
• W3100853638 cites W2962784846 @default.
• W3100853638 cites W2962831350 @default.
• W3100853638 cites W2963391340 @default.
• W3100853638 cites W2963779510 @default.
• W3100853638 cites W2963780317 @default.
• W3100853638 cites W2970385240 @default.
• W3100853638 cites W3012288838 @default.
• W3100853638 cites W3043292271 @default.
• W3100853638 cites W3102637839 @default.
• W3100853638 cites W3103229763 @default.
• W3100853638 cites W3104625821 @default.
• W3100853638 doi "https://doi.org/10.1515/acv-2019-0081" @default.
• W3100853638 hasPublicationYear "2020" @default.
• W3100853638 type Work @default.
• W3100853638 sameAs 3100853638 @default.
• W3100853638 citedByCount "2" @default.
• W3100853638 countsByYear W31008536382021 @default.
• W3100853638 countsByYear W31008536382022 @default.
• W3100853638 crossrefType "journal-article" @default.
• W3100853638 hasAuthorship W3100853638A5027009955 @default.
• W3100853638 hasAuthorship W3100853638A5039149789 @default.
• W3100853638 hasBestOaLocation W31008536381 @default.
• W3100853638 hasConcept C114614502 @default.
• W3100853638 hasConcept C132369183 @default.
• W3100853638 hasConcept C134306372 @default.
• W3100853638 hasConcept C138885662 @default.
• W3100853638 hasConcept C14036430 @default.
• W3100853638 hasConcept C17744445 @default.
• W3100853638 hasConcept C199539241 @default.
• W3100853638 hasConcept C2776650193 @default.
• W3100853638 hasConcept C2780009758 @default.
• W3100853638 hasConcept C2780813799 @default.
• W3100853638 hasConcept C33923547 @default.
• W3100853638 hasConcept C41008148 @default.
• W3100853638 hasConcept C41895202 @default.
• W3100853638 hasConcept C62354387 @default.
• W3100853638 hasConcept C77088390 @default.
• W3100853638 hasConcept C78458016 @default.
• W3100853638 hasConcept C86803240 @default.
• W3100853638 hasConceptScore W3100853638C114614502 @default.
• W3100853638 hasConceptScore W3100853638C132369183 @default.
• W3100853638 hasConceptScore W3100853638C134306372 @default.
• W3100853638 hasConceptScore W3100853638C138885662 @default.
• W3100853638 hasConceptScore W3100853638C14036430 @default.
• W3100853638 hasConceptScore W3100853638C17744445 @default.
• W3100853638 hasConceptScore W3100853638C199539241 @default.
• W3100853638 hasConceptScore W3100853638C2776650193 @default.
• W3100853638 hasConceptScore W3100853638C2780009758 @default.
• W3100853638 hasConceptScore W3100853638C2780813799 @default.
• W3100853638 hasConceptScore W3100853638C33923547 @default.
• W3100853638 hasConceptScore W3100853638C41008148 @default.
• W3100853638 hasConceptScore W3100853638C41895202 @default.
• W3100853638 hasConceptScore W3100853638C62354387 @default.
• W3100853638 hasConceptScore W3100853638C77088390 @default.
• W3100853638 hasConceptScore W3100853638C78458016 @default.
• W3100853638 hasConceptScore W3100853638C86803240 @default.
• W3100853638 hasIssue "3" @default.
• W3100853638 hasLocation W31008536381 @default.
• W3100853638 hasLocation W31008536382 @default.
• W3100853638 hasOpenAccess W3100853638 @default.
• W3100853638 hasPrimaryLocation W31008536381 @default.
• W3100853638 hasRelatedWork W1516195074 @default.
• W3100853638 hasRelatedWork W1519092155 @default.
• W3100853638 hasRelatedWork W2118736929 @default.
• W3100853638 hasRelatedWork W2580267619 @default.
• W3100853638 hasRelatedWork W2891893399 @default.
• W3100853638 hasRelatedWork W2947222398 @default.
• W3100853638 hasRelatedWork W2953190535 @default.
• W3100853638 hasRelatedWork W4289548859 @default.
• W3100853638 hasRelatedWork W4297612377 @default.
• W3100853638 hasRelatedWork W4301408533 @default.
• W3100853638 hasVolume "15" @default.
• W3100853638 isParatext "false" @default.
• W3100853638 isRetracted "false" @default.
• W3100853638 magId "3100853638" @default.

• next